Unified analytical solution for dynamic elastic buckling of beams for various boundary conditions and loading rates

2012 ◽  
Vol 56 (1) ◽  
pp. 60-69 ◽  
Author(s):  
Phani Motamarri ◽  
Srinivasan Suryanarayan
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Elastic Buckling ◽  
Loading Rates ◽  
Various Boundary Conditions

scholarly journals ANALYTICAL SOLUTION OF THE EQUATION OF CONDUCTIVITY FOR VARIOUS BOUNDARY CONDITIONS

2019 ◽  
Vol 2019 (4) ◽  
pp. 33-37
Author(s):  
Vadim Krys'ko ◽  
Olga Saltykova ◽  
Alexey Tebyakin
Keyword(s):  
Analytical Solution ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Solution Method ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Two Dimensional ◽  
Various Boundary Conditions ◽  
The Finite Difference Method

The aim of the work is to obtain an analytical solution of the heat equation for various boundary conditions in the case of a two-dimensional body. As a solution method, the method of variational iterations is used. In the work, both an analytical and a numerical solution of the problem are obtained for the boundary conditions of various types and taking into account the internal heat source. To obtain a numerical solution, the finite difference method was used. The results are compared and the conclusion is made on the reliability of the decisions.

Three-Dimensional Analytical Solution for Hybrid Multilayered Piezoelectric Plates

1999 ◽  
Vol 67 (3) ◽  
pp. 558-567 ◽  
Author(s):  
S. S. Vel ◽  
R. C. Batra
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Laminated Plates ◽  
The Body ◽  
Rectangular Plates ◽  
Laminated Plate ◽  
Various Boundary Conditions ◽  
Linear Piezoelectricity ◽  
Piezoelectric Plates

Analytical solutions for the static three-dimensional deformations of multilayered piezoelectric rectangular plates are obtained by using the Eshelby-Stroh formalism. The laminated plate consists of homogeneous elastic or piezoelectric laminae of arbitrary thicknesses. The equations of static, linear, piezoelectricity are exactly satisfied at every point in the body. The analytical solution is in terms of an infinite series; the continuity conditions at the interfaces and boundary conditions at the edges are used to determine the coefficients. The formulation admits different boundary conditions at the edges and is applicable to thick and thin laminated plates. Results are presented for thick piezoelectric plates with two opposite edges simply supported and the other two subjected to various boundary conditions. [S0021-8936(00)01803-1]

Upon Impact Numerical Modeling of Foam Materials

2017 ◽  
Vol 54 (2) ◽  
pp. 195-202
Author(s):  
Vasile Nastasescu ◽  
Silvia Marzavan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
General Character ◽  
Foam Material ◽  
Various Boundary Conditions ◽  
Specific Behaviour

The paper presents some theoretical and practical issues, particularly useful to users of numerical methods, especially finite element method for the behaviour modelling of the foam materials. Given the characteristics of specific behaviour of the foam materials, the requirement which has to be taken into consideration is the compression, inclusive impact with bodies more rigid then a foam material, when this is used alone or in combination with other materials in the form of composite laminated with various boundary conditions. The results and conclusions presented in this paper are the results of our investigations in the field and relates to the use of LS-Dyna program, but many observations, findings and conclusions, have a general character, valid for use of any numerical analysis by FEM programs.

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